The small parameter method in the problem of the lateral surface shape of the vertical liquid bridge between planes

摘要

The article is devoted to the study of the shape of the vertical liquid bridge between two solid planes with take into account the gravity force. The variation problem statement is given. The parametric form of solution presentation is used. The solution is constructed as a series in powers of a small Bond number. An algorithm for finding zeroth and the subsequent approximations is proposed. A non-uniqueness of the solution is detected. There may be several different profiles of its lateral surface for a fixed height of the liquid bridge. The dependence of the solutions number on the liquid bridge height has been analyzed.